Symmetric singular boundary method for potential problems with mixed boundary conditions

Abstract

The paper presents a symmetric formulation of the singular boundary method (SBM) for potential problems, whose resultant interpolation matrix is symmetric irrespective of boundary conditions. The SBM is a recent strong-form boundary discretization numerical technique, which is meshless, integration-free, and easy-to-implement. In stark contrast to the method of fundamental solution that requires the fictitious boundary outside physical domain to avoid the singularity of fundamental solution, the SBM can place source points, which coincide with collocation points, on the real physical boundary via the concept of origin intensity factor. The proposed symmetric formulation preserves all the merits of the SBM. The novel idea behind this study is that the unknown solution is represented by both the single and double layer potentials compared with the single layer potential in the original SBM. Numerical solution of three-dimensional potential and two-dimensional fluid flow and heat transfer problems demonstrates the utility and validity of the present SBM symmetric formulation.